This invention relates to a process control method and control system using the fuzzy theory.
In the conventional process control, the transition of the amount of a process to be controlled after lapse of unit time is predicted by the observation of the past trend of time-sequential change of different amount of process and by the method of least squares and used to determine the amount of control for the amount of process. Also, as is disclosed in, for example, Japanese Patent Laid-open Gazette No. 204707/1984 and No. 234405/1986, another conventional process control is proposed which employs the fuzzy theory for inferring the situations of process and determining the amount of control by evaluating the measured values from different process-amount sensors on the basis of operator's transcendental information.
The former conventional process control only makes the next prediction in a time-sequential manner, and the latter conventional process control determines the amount of control by the evaluation based on the transcendental information relative to absolute amount. Therefore, these conventional process control methods have the drawback that the control cannot follow an abrupt change of local primary factors associated with the process action.
On the other hand, the qualitative inference researched by J. de Kleen et al. has recently been given attention as one method of providing a model for a human to understand the phenomena in the natural world (see "Qualitative Physics Based on Confluences" J. de Kleer and J. S. Brown, Artificial Intelligence 24, 1, pp. 7-83, 1984). In this qualitative inference, three values of +, 0, - called qualitative values, not quantative values are used. The variable is called as the qualitative variable designated by [X]. Also, the differentiation dx/dt to be used for expressing the action of a system is represented by .differential.X and takes three values +, 0, - as does the variable [X]. Since a quantative equation is normally given, it must be converted into a qualitative equation. For example, the amount of flow, Q from the outlet of a tube having a cross-section A and an outflow coefficient C is expressed as ##EQU1## where P is the pressure and p is the volume density of liquid. If C and p are constants, the differentiation of this equation is given as ##EQU2## These two quantative equations are converted into the following qualitative equations. ##EQU3## When P or A makes absolute displacement relative to a constant (landmark, which will be described later) to achieve a qualitative value, this equation becomes a differential equation. In this example, however, since P and A can be considered to be constants having positive qualitative values, the expression of EQU .differential.Q=.differential.A+.differential.P
can be obtained.
The process to solve a qualitative equation is the qualitative inference and comprises an operation called propagation for assigning a qualitative value to the qualitative variable at a time point and an operation called a prediction for determining the next condition. In most cases, the qualitative values of the qualitative variable take three or more intervals relative to some constants called landmark. When a set of intervals covering real number space (I.sub.0, I.sub.1, I.sub.3 . . . I.sub.m) is represented by Q, the qualitative variable is expressed by [X].sub.Q, and takes the following values. ##EQU4## When the landmark is only a, ##EQU5## When a=0, the affix is omitted as ##EQU6## "+" can be considered as the name of the interval, X&gt;0. For realization of system, in most cases, states for each landmark are considered, or the form of [X-a] is reduced to and three values (+, 0, -) are used in calculation.
The method of calculation using qualitative values (+, 0, -) is shown in FIGS. 20 and 21. The propagation is made by determining the valuable within the qualitative equation on the basis of the figures. The prediction is performed on the basis of EQU [X(t.sub.n)]=[X(t.sub.n-1)+.differential.X(t.sub.n-1)]
It is uncertain how many times .differential.X of "+" is added to one having qualitative value "-" to reach "0" or "+". Thus, the individual problems must be considered for the determination.
This qualitative reasoning is still at the research stage, and no approaches are established in many aspects such as way to make equations, control of inference and execution of computation. Therefore, it is difficult for the qualitative inference to be applied to practical models.